Shi Yan, Chan Chi Hou
School of Electronic Engineering, Xidian University, Xi'an, Shaanxi 710071, China.
J Opt Soc Am A Opt Image Sci Vis. 2010 Feb 1;27(2):308-18. doi: 10.1364/JOSAA.27.000308.
In this paper, we present the multilevel Green's function interpolation method (MLGFIM) for analyses of three-dimensional doubly periodic structures consisting of dielectric media and conducting objects. The volume integral equation (VIE) and surface integral equation (SIE) are adopted, respectively, for the inhomogeneous dielectric and conducting objects in a unit cell. Conformal basis functions defined on curvilinear hexahedron and quadrilateral elements are used to solve the volume/surface integral equation (VSIE). Periodic boundary conditions are introduced at the boundaries of the unit cell. Computation of the space-domain Green's function is accelerated by means of Ewald's transformation. A periodic octary-cube-tree scheme is developed to allow adaptation of the MLGFIM for analyses of doubly periodic structures. The proposed algorithm is first validated by comparison with published data in the open literature. More complex periodic structures, such as dielectric coated conducting shells, folded dielectric structures, photonic bandgap structures, and split ring resonators (SRRs), are then simulated to illustrate that the MLGFIM has a computational complexity of O(N) when applied to periodic structures.
在本文中，我们提出了一种用于分析由电介质和导电物体组成的三维双周期结构的多级格林函数插值方法（MLGFIM）。对于单位晶胞中的非均匀电介质和导电物体，分别采用体积积分方程（VIE）和表面积分方程（SIE）。定义在曲线六面体和四边形单元上的共形基函数用于求解体积/表面积分方程（VSIE）。在单位晶胞的边界处引入周期性边界条件。通过埃瓦尔德变换加速空间域格林函数的计算。开发了一种周期性八叉树方案，以使MLGFIM能够适用于双周期结构的分析。首先通过与公开文献中的已发表数据进行比较来验证所提出的算法。然后对更复杂的周期结构，如介质涂层导电壳、折叠介质结构、光子带隙结构和分裂环谐振器（SRR）进行模拟，以说明MLGFIM应用于周期结构时具有O(N)的计算复杂度。
